{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CT4Z6XKBB5KCSOMEWDT2UIO4JR","short_pith_number":"pith:CT4Z6XKB","schema_version":"1.0","canonical_sha256":"14f99f5d410f54293984b0e7aa21dc4c4b895a1331891dbcb4e67b278a743b35","source":{"kind":"arxiv","id":"1311.4932","version":4},"attestation_state":"computed","paper":{"title":"The semiclassical zeta function for geodesic flows on negatively curved manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Faure, Masato Tsujii","submitted_at":"2013-11-20T01:03:45Z","abstract_excerpt":"We consider the semi-classical (or Gutzwiller-Voros) zeta function for $C^\\infty$ contact Anosov flows. Analyzing the spectrum of transfer operators associated to the flow, we prove, for any $\\tau>0$, that its zeros are contained in the union of the $\\tau$-neighborhood of the imaginary axis, $|\\Re(s)|<\\tau$, and the region $\\Re(s)<-\\chi_0+\\tau$, up to finitely many exceptions, where $\\chi_0>0$ is the hyperbolicity exponent of the flow. Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.4932","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-20T01:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"5cf658cab01fc5f24f553198e4de66982fde1b94538f4d93e29457a1992f92f2","abstract_canon_sha256":"e40c1990673cfcc3d813de9ecba9bd5bc906689abe2219848fbe44d716c6e17b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:14.293373Z","signature_b64":"Eu2X24emy3H3ve97m07DXmroEndBy5Rkd6BAlZCLCPPtxazYRJKG/70ztqbZBQUrDV6pkbrbqu5WlHnIzSVuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14f99f5d410f54293984b0e7aa21dc4c4b895a1331891dbcb4e67b278a743b35","last_reissued_at":"2026-05-18T01:02:14.292601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:14.292601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The semiclassical zeta function for geodesic flows on negatively curved manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Faure, Masato Tsujii","submitted_at":"2013-11-20T01:03:45Z","abstract_excerpt":"We consider the semi-classical (or Gutzwiller-Voros) zeta function for $C^\\infty$ contact Anosov flows. Analyzing the spectrum of transfer operators associated to the flow, we prove, for any $\\tau>0$, that its zeros are contained in the union of the $\\tau$-neighborhood of the imaginary axis, $|\\Re(s)|<\\tau$, and the region $\\Re(s)<-\\chi_0+\\tau$, up to finitely many exceptions, where $\\chi_0>0$ is the hyperbolicity exponent of the flow. Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4932","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.4932","created_at":"2026-05-18T01:02:14.292705+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4932v4","created_at":"2026-05-18T01:02:14.292705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4932","created_at":"2026-05-18T01:02:14.292705+00:00"},{"alias_kind":"pith_short_12","alias_value":"CT4Z6XKBB5KC","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CT4Z6XKBB5KCSOME","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CT4Z6XKB","created_at":"2026-05-18T12:27:40.988391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR","json":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR.json","graph_json":"https://pith.science/api/pith-number/CT4Z6XKBB5KCSOMEWDT2UIO4JR/graph.json","events_json":"https://pith.science/api/pith-number/CT4Z6XKBB5KCSOMEWDT2UIO4JR/events.json","paper":"https://pith.science/paper/CT4Z6XKB"},"agent_actions":{"view_html":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR","download_json":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR.json","view_paper":"https://pith.science/paper/CT4Z6XKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4932&json=true","fetch_graph":"https://pith.science/api/pith-number/CT4Z6XKBB5KCSOMEWDT2UIO4JR/graph.json","fetch_events":"https://pith.science/api/pith-number/CT4Z6XKBB5KCSOMEWDT2UIO4JR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/action/storage_attestation","attest_author":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/action/author_attestation","sign_citation":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/action/citation_signature","submit_replication":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/action/replication_record"}},"created_at":"2026-05-18T01:02:14.292705+00:00","updated_at":"2026-05-18T01:02:14.292705+00:00"}